Аннотация:We show that the affine cones over any Fano–Mukai fourfold of genus 10 are flexible in the sense of [1]. In particular, the automorphism group of such a cone acts highly transitively outside the vertex. Furthermore, any Fano–Mukai fourfold of genus 10, with one exception, admits a covering by open charts isomorphic to $$\mathbb A^4$$.